Since the advent of public-key cryptography, numerous public-key cryptographic systems have been proposed. Today, only three types of systems are still considered secure and efficient. These systems include integer factorization systems, discrete logarithm systems and elliptic curve cryptography (ECC) systems. The security afforded by integer factorization rests on the difficulty of factoring a large product of two prime numbers. The security of discrete logarithm systems rests on the difficulty of solving the discrete logarithm problem (DLP). The security of ECC systems rests on the difficulty of solving the elliptic curve DLP (ECDLP) problem, which amounts to finding a log in a group of points defined on an elliptic curve over a prime field. ECC's advantage over other systems is that its inverse operation gets harder, faster, against increasing key length, making it suitable for portable devices having small form factors with limited power and memory.
Cryptographic systems, and particularly stream ciphers, often use pseudorandom number generators to provide sequences of random numbers. Such random number generators can produce, at most, only 2k different output values, where k is the number of bits used to represent internal state data. The pseudorandom number generator often is initialized in an arbitrary state of a repeating sequence of states (i.e., a cycle) as some function of a keyword or key phrase. Thus, an arbitrary initialization of a pseudorandom sequence may result in a short cycle or pattern of different output values that could repeat during a long message or session. These repeated patterns make pseudorandom number generators vulnerable to automated attacks. To prevent patterns from occurring, longer sequences (large k values) can be used. However, for devices having small form factors (e.g., media players, mobile phones, etc.), power and memory constraints limit the length of the random number sequences that can be generated, resulting in an increased risk that detectable patterns will be generated.
Therefore, what is needed is a system, method and apparatus for providing random numbers of cryptographic strength that are suitable for use in cryptographic systems for small devices.